Recently, thin film techniques have been advancing. For example, semiconductor devices having various pattern structures with submicron features have been developed, such as semiconductor lasers, GaAs HEMTs (high electron mobility transistors), and HBTs (heterojunction bipolar transistors). To produce these semiconductor devices with a high degree of repeatability, particularly in compound semiconductor devices, it is important to control the thicknesses of epitaxially grown thin crystalline films.
Conventionally, thicknesses of thin films are measured in a cleaved cross-section of a sample with an SEM (scanning electron microscope). However, this method is destructive and requires etching of a sample and, therefore, cannot be used in a manufacturing line.
A non-destructive interference method of measuring layer thickness has recently been used. This method employs Fourier Transformation Infrared Spectroscopy (hereinafter referred to as FTIR) apparatus having a Fourier transformation processing function and a light dispersing spectroscopy apparatus. This method comprises irradiating a sample with infrared light having a relatively wide wavenumber range from far infrared to near infrared, having a spectrum wavenumber modulation band of 0 to 32000 cm.sup.-1 and Fourier transformation of the interference spectrum to produce a space interference waveform (hereinafter referred to as Spatialgram), thereby evaluating the thicknesses of the layers of the multi-layer film.
FIG. 4(a) is a block diagram illustrating the construction of the FTIR apparatus. In FIG. 4(a), reference numeral 13 designates a Michelson interferometer emitting an interference light flux that is modulated in time. Numeral 26 designates a photometry system for spectrometry of the reflected light obtained by irradiating a sample with measuring light from the interferometer 13. Numeral 150 designates a spectroscopy apparatus comprising the Michelson interferometer 13 and the photometry system 26 for continuous spectrometry of the reflected light from the multi-layer film in a range from visible light to the far infrared. Numeral 200 designates a data processing apparatus for Fourier transformation of the electrical signal that is obtained from the light measurement by the photometry system 26 of the spectroscopy apparatus 150 and further analysis of the signal.
FIG. 4(b) is a flowchart schematically illustrating the data processing performed by the FTIR apparatus. In the figure, reference numeral 200a designates measuring the interference light intensity waveform. Numeral 200b designates Fourier transformation of the interference light intensity waveform measured at the step 200a. Numeral 200c designates reverse Fourier transformation of the result obtained by the Fourier transformation at the step 200b.
FIG. 5 is a block diagram illustrating the construction of the data processing apparatus. In FIG. 5, reference numeral 2001 designates an interference light intensity waveform measuring section for measuring the interference light intensity waveform from the output of the detector included in the photometry system. Numeral 2002 designates a memory for storing the measured result of the interference light intensity waveform measuring part 2001. Numeral 2003 designates a Fourier transformation means for Fourier transformation of the output of the interference light intensity waveform measuring part 2001 and of the data from the memory 2002. Numerals 2004 and 2005 designate memories for storing the Fourier transformed results from the Fourier transformation means 2003. Numeral 2006 designates a subtracter for obtaining the difference between the output of the two memories 2004 and 2005. Numeral 2007 designates a filter for filtering the output of the subtracter 2006. Numeral 2008 designates a reverse Fourier transformation means for reverse Fourier transformation of the output of the filter 2007. Numeral 2009 designates a burst interval measuring means for measuring the burst interval from the output of the reverse Fourier transformation means 2008.
The operation of the apparatus is described with reference to FIGS. 4(b) and 5. First of all, the sample is irradiated with the interference light flux emitted from the Michelson interferometer 13 and the light reflected by the sample is received by the photodetector included in the reflection light photometry system 26. The received light is converted into an electrical signal as an interference light intensity waveform (at step 200a).
This interference light intensity waveform is Fourier transformed (at step 200b) and is subjected to a predetermined filtering process and the filtered result is reverse Fourier transformed to produce a Spatialgram (at step 200c). From the interval between burst peaks in this Spatialgram, the thickness of a layer is determined.
The interference light intensity waveform including the thickness information for the thin multi-layer film is measured by the interference light intensity waveform measuring part 2001 from the electrical signal that is forwarded from the detector in the photometry system. This interference light intensity waveform is Fourier transformed by the Fourier transformation means 2003, resulting in a spectrum. Prior to the measurement of the interference light intensity waveform for the sample, the interference light intensity waveform data are measured by the same method on a standard sample which is produced by, for example, evaporating gold on a semiconductor substrate and these data are stored in the memory 2002. Then, the interference light intensity waveform data of the standard sample are read out from the memory 2002 as required and Fourier transformed, resulting in the spectrum. The spectrum of the thin multi-layer film sample and the spectrum of the standard sample are stored in the memories 2004 and 2005, the contents of the memories are input to the subtracter 2006 to obtain a difference spectrum, and the difference spectrum in the noise wavenumber band is subjected to filtering in the filter 2007 to remove noise. The difference spectrum obtained is reverse Fourier transformed by the reverse Fourier transformation means 2008, thereby producing a Spatialgram called a Kepstrum. In the Kepstrum, there are bursts because all the respective reflected light components are intensified by interfering with each other at positions where the optical path length differences due to differences between the positions of the moving mirror coincide with the optical path length differences between the respective reflected light components from the sample. These distances between respective bursts correspond to the optical path length differences between respective reflection light components. Accordingly, by measuring the distance between the bursts with the burst interval measuring means 2009, the optical path length differences and the thicknesses of respective layers are obtained.
By performing the waveform analysis on the Kepstrum obtained utilizing the Fourier analysis, the thicknesses of respective layers of the thin multi-layer film are obtained.
This prior art film thickness measuring method employing the FTIR method will be described with reference to FIG. 10 showing a conceptual diagram of the optical system. In FIG. 10, reference numeral 10 designates a light source emitting light irradiating a sample. Reference numeral 12 designates a non-spherical mirror converting the light from the light source 10 into a parallel light beam. Numeral 14 designates a beam splitter for dividing the parallel light beam from the non-spherical mirror 12 into two parts. Reference numeral 15 designates a fixed mirror reflecting the light transmitted through the beam splitter 14. Reference numeral 16 designates a moving mirror reflecting the light reflected from the beam splitter 14. Numeral 17 designates a driver for scanning the moving mirror 16 at a constant speed. Reference numeral 13 designates a Michelson interferometer generating an interference light flux and comprising the beam splitter 14, the fixed mirror 15, the moving mirror 16, and the driver 17.
Reference numeral 27 designates an aperture for limiting the magnitude of the interference light from the beam splitter 14 of the Michelson interferometer 13. Reference numeral 28 designates a plane mirror reflecting the parallel light beam from the aperture 27 to change its direction. Reference numeral 11 designates a sample irradiated by the parallel light beam from the plane mirror 28. Reference numeral 29 designates a plane mirror reflecting the parallel light beam reflected from the sample 11 to change its direction. Reference numeral 30 designates a non-spherical mirror on which the parallel light beam from the plane mirror 29 is incident. Reference numeral 21 designates a detector for detecting the light collected by the non-spherical mirror 30. Reference numeral 26 designates a reflection photometry system for metering the sample comprising the aperture 27, the plane mirror 28, the sample 11, the plane mirror 29, and the non-spherical mirror 30.
The light emitted from the light source 10 is converted into a parallel light beam by the non-spherical mirror 12 and is introduced into the Michelson interferometer 13. The Michelson interferometer 13 includes the beam splitter 14 for dividing the incident parallel light beam into two parts, the fixed mirror 15 reflecting the light transmitted by the beam splitter 14, and the moving mirror 16 reflecting the light reflected from the beam splitter 14 which is scanned at a constant speed by the driver 17. The transmitted light and the reflected light of the beam splitter 14 are respectively reflected by the fixed mirror 15 and the moving mirror 16 and again returned to the beam splitter 14 and synthesized on that plane to interfere with each other. This interference light is an interference light flux that is modulated in time by the constant speed scanning of the moving mirror 16 and exits at the side of the aperture 27 for reflection photometry. The parallel light beam from the Michelson interferometer 13 is reformed to an arbitrary magnitude by the aperture 27 and then changes direction at the plane mirror 28. This parallel light beam irradiates the surface of the sample 11. The light reflected from the sample 11 is subjected to interference due to the multiple film construction of the sample 11, changes its direction at the plane mirror 29, and is collected on the light receiving surface of the detector 21 by the non-spherical mirror 30.
FIG. 6 shows the reflection light paths of one-dimensional light reflected at respective layers of the light flux incident on the sample by the reflection photometry system of the Michelson interferometer shown in FIG. 10. In FIG. 6, reference numeral 1 designates a semiconductor substrate and reference numerals 2, 3, and 4 designate thin semiconductor films successively laminated on the semiconductor substrate 1 in this order. Reference numeral 5 designates light incident on the sample from the Michelson interferometer. Numeral 6 designates light reflected from the surface of the thin semiconductor film 4 at the uppermost layer of the sample. Numeral 7 designates light reflected at the interface between the thin semiconductor film 4 and the thin semiconductor film 3. Numeral 8 designates light reflected at the interface between the thin semiconductor film 3 and the thin semiconductor film 2. Numeral 9 designates light reflected at the interface between the thin semiconductor film 2 and the semiconductor substrate 1.
Suppose that the film thicknesses and refractive indices of the thin semiconductor films 2, 3, and 4 are respectively, (d.sub.1, n.sub.1), (d.sub.2, n.sub.2), and (d.sub.3, n.sub.3) and the refractive index of the substrate 1 is n.sub.s. The light reflected by respective layers produces phase differences due to different respective optical path lengths and are synthesized at the surface of the sample 11 and interfere with each other. The optical path length difference .delta..sub.i of the reflected light component reflected at the interface between the i-th layer and (i+1)-th layer for the reflected light component 5 at the surface of the sample 11 is given by the following formula (1). ##EQU1## The thicknesses of the respective layers are obtained from an analysis of the interference light intensity waveform of the reflected light utilizing the phase difference on the basis of the .delta..sub.i.
Generally, a method of evaluating layer thickness from the analysis of the interference fringes of the reflected interference spectrum of a thin film is adopted. This method is effective in a case where the film comprises a single layer. However, when the film comprises a plurality of layers, it is quite difficult and not practical to separate and analyze each of the fringes. Therefore, the Fourier analysis is utilized, i.e., the film reflection interference spectrum is filtered to remove noise, and the filtering result is reverse Fourier transformed to obtain a Spatialgram corresponding to the moving distance of the moving mirror 16. In the Spatialgram, respective bursts appear because all the light beams intensify each other by interference at positions where the optical path difference corresponding to the scanning position of the moving mirror 16 coincides with the optical path length difference of respective reflection light components. This intensification is represented in formula (1), and the distances between respective bursts correspond to the optical path length differences between respective reflected light beams.
FIG. 11 shows a Spatialgram obtained from the reflected light shown in FIG. 6. The abscissa represents the position of the moving mirror 16 and the ordinate represents reflected light interference intensity. In the figure, the center burst 31 corresponding to the reflected light component 6 at the surface of the sample 11 appears as the origin and the symmetrical reflected light components 7, 8, and 9 of respective layers produce respective side burst peaks 32, 33, and 34. Provided that the distances from the center burst 31 to the respective side burst peaks are Li (i=1, 2, 3), an optical path length difference .delta..sub.i between the respective reflected light components coincides with 2L.sub.i, a sum of the incident path and the reflected path to and from the moving mirror 16. Therefore, the following equation is obtained from the above-described formula (1): ##EQU2##
By performing a waveform analysis of the Kepstrum that is obtained by reverse Fourier transformation of the reflected interference light of the multi-layer film, it is possible to obtain thickness information for the respective layers of the multi-layer film.
However, in this prior art method, the thin film measurement limit (d.sub.limit) is determined by the formula (3) according to the photometry wavenumber range .DELTA.. EQU d.sub.limit =1/(2.multidot..DELTA..multidot.n) (3)
This is equivalent to the fringe interval in the interference wavenumber in wavenumber (or wavelength) space of the single layer film having a thickness d and a refractive index n, corresponding to 1/(2.multidot.d.multidot.n) and shows that the thickness separation limit in the Spatialgram for a multi-layer film requires information on the interference components of respective films corresponding to one interference fringe in wavenumber space.
Accordingly, the thickness measuring limit of a thin film is determined by the photometry wavenumber range that, in turn, is determined by the photometry system and the absorption of the material of the measured multi-layer film.
With respect to the transmission characteristics of the light of the photometry system, Japanese Published Patent Application Hei. 5-302816 discloses a system that is responsive to a wider wavenumber range because of an improvement in the optical parts and employment of composite materials having different transmission wavenumber bands. For example, a light source, an optical system, and a light receiving part for common use have wavenumber characteristic ranges mutually overlapping each other.
FIG. 12(a) shows construction of an optical detector in a thin semiconductor multi-layer film thickness measuring apparatus having a light source, an optical system, and a light detector for common use that have wavenumber characteristic ranges mutually overlapping each other. In the figure, reference numeral 21a designates a beam splitter for splitting the light beam collected by the light collecting mirror. Reference numerals 21b and 21c designate a mercury cadmium telluride (MCT) detector and a silicon detector that convert the light divided by the beam splitter 21a into an electrical signal. Reference numeral 21d designates an electrical signal synthesizer circuit for synthesizing electrical signals obtained from the MCT detector 21b and the silicon detector 21c, respectively.
By constructing the photodetector as such, the detection sensitivity of the detector amounts to the sum of the sensitivity characteristics of the MCT detector and the silicon detector, whereby sensitivity characteristics that cannot be achieved with a single photodetector are obtained.
As shown in FIG. 12(b), the MCT detector 21b can be replaced by a low cost tri-glycine sulfate (TGS) detector 21e. In this case, since parts for cooling the MCT detector are not required, the apparatus is simplified and cost is reduced.
FIG. 13 shows an improvement of the photodetector shown in FIG. 12(a). The MCT detector 21b and the Si detector 21c are fixed in the same plane with epoxy resin or the like in a liquid nitrogen cooler 50 that cools the MCT detector 21b. A light beam collected by a collecting mirror 30 enters directly into both the MCT detector 21b and the Si detector 21c and is detected at the same time. Then, the electrical signals output from the detectors are synthesized in the electrical signal synthesizer circuit 21d.
Employing such a construction, influences due to the transmission characteristic of the beam splitter disappear and the photometric wavenumber ranges of both the detectors 21b and 21c are obtained more immediately, improving the photometry precision.
In FIG. 14, three kinds of photodetectors are employed as a complex photodetector. By arranging a germanium (Ge) detector 44 in the same plane as the MCT detector 21b and the Si detector 21c, the sensitivity valley of the synthesized sensitivity characteristic of the MCT detector 21b and Si detector 21c is compensated. It is desirable to employ an MCT detector having a larger area than the other detectors because the MCT detector 21b is inferior in sensitivity to other detectors. Such a construction provides a photodetector having a high sensitivity and a wide photometric wavenumber range.
FIG. 15 is a chart of wavenumber characteristic ranges of various kinds of light sources, photodetectors, and beam splitters. According to the sum of the wavenumber characteristic ranges of both the MCT detector and the Si detector, the possibility of detection over a wide range from around 25000 cm.sup.-1 to 500 cm.sup.-1 is presented. This suggests that light in a range from visible light (blue light) to far infrared light is possibly detected by a complex photodetector incorporating an MCT detector and an Si detector for optimization. In FIG. 15, Subscripts A, B, and C in parentheses represent photodetectors comprising the same materials but with different composition ratios.
FIGS. 16(a) and 16(b), respectively, show light transmission members corresponding to the beam splitter. In both FIGS. 16(a) and 16(b), reference numeral 54 designates a region comprising calcium fluoride (CaF.sub.2) and numeral 55 designates a region comprising quartz (SiO.sub.2). By employing two materials having different light transmission bands for respective halves of the light transmission area of the beam splitter, the characteristic wavenumber range of the beam splitter is enlarged to the sum of the respective characteristic wavenumber ranges of the two materials. In the above-described construction, according to the column of the beam splitter in the table of FIG. 15, the aggregate wavenumber characteristic range of the beam splitter employing calcium fluoride (CaF.sub.2) and quartz (SiO.sub.2) is approximately from 25000 cm.sup.-1 to 2000 cm.sup.-1. In addition, the construction of FIG. 16(b) having more than two different materials for the respective sectioned areas arranged alternatingly can reduce the destruction of wavefronts of a transmitted light beam to a larger extent than the construction of FIG. 16(a) having two different materials for the half-sectioned areas, thereby providing a more uniform in-plane beam intensity.
The beam splitter may comprise three materials as shown in FIG. 16(c). In the construction of FIG. 16(c), a calcium fluoride (CaF.sub.2) region 54, a quartz (SiO.sub.2) region 55, and a potassium bromide (KBr) region 52 are arranged at the triple-sectioned areas of the light transmission region. According to the beam splitter column of FIG. 15, the beam splitter including calcium fluoride, quartz, and potassium bromide enables optical measurement in a wavenumber range of approximately from 25000 cm.sup.-1 to 400 cm.sup.-1, thereby enlarging the long wavelength band to a larger extent than the construction employing two materials shown in FIGS. 16(a) and 16(b).
In addition, a system in which the light source is improved as shown in FIG. 17 may be employed. In FIG. 17, light beams from a tungsten halogen lamp 10a and a nichrome luminous lamp 10c are collected by collecting mirrors 10b and 10d, respectively, and are synthesized through a beam splitter 10e. The synthesized beam is reformed by an aperture 10f as a collected light source and introduced to the collimating mirror 12. Since the optical path lengths from the aperture 10f to the respective lamps 10a and 10c are equal to each other, the respective light beams from the lamps that are synthesized at the beam splitter 10e have the same wavefronts at the aperture 10f and become one parallel light beam at the collimating mirror 12.
By combining the tungsten halogen lamp 10a and the nichrome luminous lamp 10c and synthesizing the outgoing light, it is possible to irradiate a sample with a light beam of the wavenumber range from 25000 cm.sup.-1 to 200 cm.sup.-1 as shown in the light source column of FIG. 15.
Japanese Published Patent Application Hei. 3-110405 discloses an improvement in which the light irradiates a substrate as a parallel light beam, whereby the variation in the light incident on the sample and variations in the incident surface are reduced, and a Kepstrum including correct information for the thin multi-layer film is obtained, as shown in FIG. 10.
Japanese Published Patent Application Hei. 4-66806 discloses a data processing apparatus for processing a signal that is converted into an electrical signal by a light detector. In this apparatus, the measured photometered spectrum to be subjected to a Fourier transformation is supplemented with data of a constant value in the wavenumber bands exceeding the high band side and the low band side, whereby generation of a quasi-peak is suppressed.
FIG. 18 shows a flowchart illustrating the content of the processing performed by the data processing apparatus supplementing data of a constant value prior to the Fourier transformation. In FIG. 18, the film interference spectrum is measured by the FTIR apparatus according to a conventional method (at step 100a). The low frequency component included in the thus obtained spectrum is removed (at step 101a), resulting in a film interference spectrum as shown in FIG. 19.
In this embodiment, spectrum data that is obtained by processing the waveform data (at step 101b) is added. More particularly, as shown in FIG. 20, the reflection interference spectrum intensity data at the left side (wavenumber .sigma..sub.1 =12000 cm.sup.-1) of the interference spectrum is supplemented as interference spectrum intensity data from O to .sigma..sub.1 cm.sup.-1, and the spectrum intensity data of the right side end in the figure (wavenumber .sigma..sub.2 =12000 cm.sup.-1)) is supplemented as reflection interference spectrum intensity data from the wavenumber .sigma..sub.max cm.sup.-1.
Subsequently, the reflection interference spectrum data after the waveform data processing is performed that is shown in FIG. 20 is Fourier transformed (at step 101c), thereby producing a Spatialgram as shown in FIG. 21 (at step 101d). The peaks of this Spatialgram are searched (at step 101d) and, from the interval between the peaks, the layer thickness is calculated (at step 101f).
When the Spatialgram shown in FIG. 21 is compared with a Spatialgram that is obtained without such data supplementation, although the reflection interference spectrum of the same wavenumber range is obtained from the same semiconductor triple-layer film, the side bursts corresponding to respective film thicknesses are significantly clarified, whereby quasi-peaks are suppressed to a great extent.
FIG. 22 shows a power spectrum corresponding to the Spatialgram shown in FIG. 21. Of course, even in FIG. 22, the peak values I, II, and III representing respective film thicknesses are much clarified and there is no obstacle to the automation of the thickness measuring operation.
Even when the Spatialgram shown in FIG. 21 is compared with a Spatialgram that is obtained without performing such data interpolation, the position of the side burst in the abscissa does not change at all. Therefore, even when the reflection interference spectrum of a relatively narrow wavenumber range is employed, an accurate thickness measurement can be performed.
Japanese Published Patent Application Hei. 4-120404 discloses subjecting a reflection spectrum that is obtained by Fourier transformation to a complex power reverse Fourier transformation, thereby clarifying the peaks by making all the burst waveforms of the same phase, whereby thickness measuring precision is improved. FIG. 23 shows a flowchart illustrating the content of the processing performed by data processing apparatus including such a complex power reverse Fourier transformation.
In FIG. 23, reference numeral 150 designates an optical system that continuously irradiates a sample with interference light flux having different wavenumbers, the sample including a thin semiconductor multi-layer film. The interference light flux reflected from the sample is detected to produce an interferogram. Reference numeral 110 designates a Fourier transformation means for Fourier transformation of the interferogram that is obtained by converting the light signal with the photodetector included in the optical system 150 to obtain a reflected light spectrum. Reference numeral 120 designates a filter for filtering the Fourier transformed signal that is obtained from the Fourier transformation means 110. Reference numeral 130 designates a complex power reverse Fourier transformation means for performing a complex power reverse Fourier transformation on the reflection spectrum that is obtained by filtering with the filter 120 to obtain a space interference waveform.
In this embodiment, the reflection spectrum that is obtained by filtering is subjected to the complex power reverse Fourier transformation by the complex power reverse Fourier transformation means 130 to obtain a space interference intensity waveform.
This complex power reverse Fourier transformation means 130 produces the space interference intensity waveform in the reverse Fourier transformation employing the composite power transformation including a cosine term and a sinusoidal term as represented by the formula (4): ##EQU3##
Next, the thickness of the sample comprising a thin semiconductor multi-layer film on a semiconductor substrate is measured and evaluated. The sample comprises a GaAs substrate on which Al.sub.x Ga.sub.1-x As (x=0.5, 0.85 .mu.m thick), Al.sub.x Ga.sub.1-x As (x=0.1, 0.1 .mu.m thick), and Al.sub.x Ga.sub.1-x As (x=0.5, 1.4 .mu.m thick) are grown. A space interference intensity waveform obtained by the complex power reverse Fourier transformation means 130 is shown in FIG. 24. In the conventional cosine reverse Fourier transformation, two burst waveforms overlap each other to produce an asymmetrical waveform so that it is difficult to find the peak position. In addition, since this asymmetrical waveform is sensitive to the filter condition in the reverse Fourier transformation and changes its shape, it is actually impossible to find the peak in this waveform and to obtain the layer thicknesses.
On the other hand, in the space interference waveform shown in FIG. 24, although the peak position interval corresponds to 0.1 .mu.m, the burst waveforms are clearly separated and a spatial interference intensity waveform that is sufficiently stable for an actual thickness measurement is obtained.
Since the space interference intensity waveform obtained by the complex power reverse Fourier transformation includes more information than that obtained by the conventional cosine reverse Fourier transformation and respective burst waveforms all have the same phases, the precision of the thickness measurement is increased. For example, in a photometering condition having a measurement limit of 0.2 .mu.m, a thickness measurement of a 0.1 .mu.m thickness is possible.
Regardless of the above-described efforts, the high frequency light transmission limit .nu..sub.h is determined by the band edge absorption of the semiconductor material to be measured while the low frequency limit .nu..sub.1 is determined by the crystalline lattice vibration absorption, thereby limiting the measured light wavenumber range .DELTA.=.nu..sub.h -.nu..sub.1 which results in a physical limit in the precision of d.sub.limit. For example, the band edge absorption wavenumber of Al.sub.x Ga.sub.1-x As (x=0.45) is 16500 cm.sup.-1, the lattice vibration absorption is about 1500 cm.sup.-1, so .DELTA. becomes 15000 cm.sup.-1. When this .DELTA. is applied in the formula (3), the is about 0.1 .mu.m. In other words, in the prior art technique, the thin film measuring limit is determined by the absorption of the semiconductor material, resulting in a limitation in the thickness measurement of about 0.1 .mu.m.